Question: Christopher is 20 years older than Vanessa. Twelve years ago, Christopher was 3 times as old as Vanessa. How old is Vanessa now?
Explanation: We can use the given information to write down two equations that describe the ages of Christopher and Vanessa. Let Christopher's current age be $c$ and Vanessa's current age be $v$ The information in the first sentence can be expressed in the following equation: $c = v + 20$ Twelve years ago, Christopher was $c - 12$ years old, and Vanessa was $v - 12$ years old. The information in the second sentence can be expressed in the following equation: $c - 12 = 3(v - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $v$ , it might be easiest to use our first equation for $c$ and substitute it into our second equation. Our first equation is: $c = v + 20$ . Substituting this into our second equation, we get the equation: $(v + 20)$ $-$ $12 = 3(v - 12)$ which combines the information about $v$ from both of our original equations. Simplifying both sides of this equation, we get: $v + 8 = 3 v - 36$ Solving for $v$ , we get: $2 v = 44$ $v = 22$.